Not only am I with the OP on this one, but I consider these terms to be too one-sided. Yes, the consumer may well have been shown cancellation terms when booking, and may even have received an Email which might allow them to calculate how much the refund should be, but there must IMHO be an awareness of what the costs of cancellation will be BEFORE accepting such blind conditions. Giving BA a blank cheque to charge "what they like" and you have accepted that before knowing the amount is absolute nonsense.

Agents being unable to calculate what the refund should be on the phone only reinforces my opinion on that. If a BA agent is incapable of calculating the refund, how the heck should a consumer be able to.

I am no lawyer, but I would doubt that these conditions are allowable in law. If a cancellation is done on this basis which would result in charges so high one would not normally accept them and instead fly the itinerary as originally booked, I would say there is cause to insist the booking is reinstated.

My experience of these back-office calculations is also variable. I have literally just in the last 30 minutes managed to complete a redemption booking change to introduce a stopover in an existing itinerary by moving the final sector back 14 days. It took 3 calls to BA and 3 different calculations of the fees/taxes change. In the end I called YouFirst and it was sorted in 15 minutes, but it should not be such a lottery over which agent you get on the line.